Question

x minus root 2 whole square - 2 X + 1 is equal to zero whether the following quadratic equation has two different real roots​

Answer 1

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Answer 2

No quadratic equation has no two different real roots​.

Step-by-step explanation:

Given : Expression $(x-\sqrt2)^2-2x+1=0$

To find : Whether the following quadratic equation has two different real roots?

Solution :

First we write expression in quadratic form,

$(x-\sqrt2)^2-2x+1=0$

$x^2+2-2\sqrt2x-2x+1=0$

$x^2-x(2\sqrt2-2)+3=0$

On comparing with general quadratic equation $ax^2+bx+c=0$

a=1, $b=-(2\sqrt2-2)$ and c=3

The nature of roots is determined by discriminant method,

$D=b^2-4ac$

$D=(-(2\sqrt2-2))^2-4(1)(3)$

$D=8+4-8\sqrt2-12$

$D=-8\sqrt2$

As D<0 which means roots are imaginary.

So, No quadratic equation has no two different real roots​.

#Learn more

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